ENDOGENOUS VS. EXOGENOUS UNCERTAINTY: ARE WE ALONE?

A colleague of mine draws the line between engineers (like myself) and economists as follows:

• An engineer believes that fellow human beings are a little dumb, but otherwise they are generally good chaps. All you have to do is to find a clever solution for them, and they will live happily ever after.
• An economist believes that fellow human beings are not dumb at all. The problem is that you cannot turn your back on them, unless you have a taste for an instant stab.

In fact, the need for analyzing the interactions between noncooperative decision makers was the driving force for the development of game theory. We will consider related issues in Section 14.3, where we investigate the role of misaligned incentives when multiple stakeholders are involved in a decision-making process. The interaction of multiple actors may also change the nature of the uncertainty involved in decision making. Simple probability models assume that uncertainty is known and fixed; if we have enough information, we can make a good decision. However, it might be the case that the very uncertainty is influenced by decisions.

Example 1.1 To illustrate, let us go once again back to the inventory management problem of Section 1.2.1. There, we used historical data to characterize demand uncertainty and planned on using that information to come up with a decision. One tough question is: Does our decision affect the demand distribution? To get the point, imagine that you stock very few items. In the long run, you will end up losing customers, not just orders. What’s even worse, maybe this will also affect the demand for other items.

In practice, there are many cases in which demand is affected by stocking decisions. At retail stores, the shelf space allocated to a product may have a remarkable effect on demand. More generally, uncertainty need not be purely exogenous, i.e., given by outside factors that are not going to change (at least in the short term); uncertainty may be partially endogenous, i.e., influenced by our actions. Representing the dependence between our decisions and uncertainty may be very difficult, but at least one should be aware of the issue.

More generally, we should consider that management decisions are made in a social context, where other people could

• React to our decisions
• Use the same information we have
• Observe our behavior to gather information

Example 1.2 To see another example in a supply chain management context, suppose that we are selling a perishable item. We start selling it in the morning, and we know that at the end of the day we will scrap what’s left. One could consider a dynamic pricing strategy, whereby price is marked down at the end of the day; after all, it seems better to recover some money even if this implies selling below cost. That’s fine, but we are not considering the possibility of strategic behavior on the part of customers. Knowing that price will be reduced, they could wait and buy at dusk, just before closing time.¹⁹ The point is that there is no separation between the set of customers who buy during the first part of the day and customers who buy later. We may apply price discrimination, i.e., asking different prices for the same product on different markets, provided they are well separated, possibly in space. The above revenue management policy is a sort of failed price discrimination strategy in time, rather than in space.

There could also be other reasons not to mark down some products. Some fresh and quickly perishable produce is not really sold for profit at retail stores. The real intent is to promote a positive image of “freshness” that has a positive impact on sales of other, more profitable items. The message would be lost by selling almost perished items in the evening.

Social issues are even more fundamental in finance. A whole discipline, behavioral finance, was born to investigate the interplay between psychology and finance. When you buy a good, you know its selling price and you may plan accordingly. However, financial markets are based on a competitive auction mechanism, so that prices depend on investors’ behavior, on their beliefs (or lack of information), and on their beliefs about other investors’ beliefs. The resulting pattern may be quite complex, and indeed it leads to bubbles and crashes. Everything is made even more complicated by deliberate trading strategies.

Example 1.3 (Short selling) A short sale is a trading strategy whereby you sell an asset, say, a stock share, that you do not own. To do so, you have to borrow that asset from someone, else. It is a strategy that makes sense if you expect the asset price to drop. To see this, assume that the current price is S₀ = $50 at time t = 0. If you sell the asset short, you borrow the asset and sell it for $50. Clearly, you will have to give the asset back to its legitimate owner at some later time t = T, which means that you will have to buy the asset at a price S_T in the future. If you are right and the asset price falls, e.g., to S_T = $40, your reward will be $10 per share.

At times of financial turmoil, wealthy speculators could do a lot of short selling, which may itself depress prices, resulting in a self-fulfilling prophecy. Selling an asset short in large volumes can lead to lower prices, even if the economic and business fundamentals of the firm are good. Uninformed traders may just follow the lead, just because they see a drop in price, even if they do not know why this is happening. A perverse feedback mechanism can be the result, and indeed short selling is sometimes prohibited, when markets are under severe pressure. The role of short sellers (the “shorts”) is actually debated, but the point here is that the interaction between actors can result in weird patterns.

A similar speculative practice is predatory trading. Suppose that you own a large amount of an asset and you know that Mr. X has to sell a large amount of the same asset, because he is running short of liquidity. You could sell the asset before Mr. X, which will result in a significant price drop, as the large trading volume will affect prices. Mr. X will have to sell, anyway, which will depress prices further. Then, you may buy the asset back at a lower price, getting back to your previous portfolio, plus some extra cash.

Empirical research is carried out to verify if certain speculative practices such as predatory trading are actually carried out at a significant level. These very empirical research lines do use a lot of statistical methods, and have a practical impact as market regulation should be devised in such a way to avoid excessive distortions. Empirical finance is beyond the scope of this book, but in the next section we analyze in more detail a somewhat stylized, yet very significant, example to see the interplay between organized markets and uncertainty.